the_tate <- readr::read_delim("data/the-tate-collection.csv", ";", escape_double = FALSE, trim_ws = TRUE)
the_tate_artists <- readr::read_csv("data/the-tate-artists.csv")BSMM-lab-2
BSMM 8740 Fall 2023
Setup
Load packages and data:
Exercises
library(magrittr) # the pipeWarning: package 'magrittr' was built under R version 4.3.1library(tidyverse) # for data wrangling + visualizationWarning: package 'tidyverse' was built under R version 4.3.1Warning: package 'ggplot2' was built under R version 4.3.1Warning: package 'tibble' was built under R version 4.3.1Warning: package 'tidyr' was built under R version 4.3.1Warning: package 'readr' was built under R version 4.3.1Warning: package 'purrr' was built under R version 4.3.1Warning: package 'dplyr' was built under R version 4.3.1Warning: package 'stringr' was built under R version 4.3.1Warning: package 'forcats' was built under R version 4.3.1Warning: package 'lubridate' was built under R version 4.3.1── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.3 ✔ readr 2.1.4
✔ forcats 1.0.0 ✔ stringr 1.5.0
✔ ggplot2 3.4.3 ✔ tibble 3.2.1
✔ lubridate 1.9.2 ✔ tidyr 1.3.0
✔ purrr 1.0.2
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ tidyr::extract() masks magrittr::extract()
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
✖ purrr::set_names() masks magrittr::set_names()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(tidymodels) # for modelingWarning: package 'tidymodels' was built under R version 4.3.1── Attaching packages ────────────────────────────────────── tidymodels 1.1.1 ──
✔ broom 1.0.5 ✔ rsample 1.2.0
✔ dials 1.2.0 ✔ tune 1.1.2
✔ infer 1.0.5 ✔ workflows 1.1.3
✔ modeldata 1.2.0 ✔ workflowsets 1.0.1
✔ parsnip 1.1.1 ✔ yardstick 1.2.0
✔ recipes 1.0.8 Warning: package 'broom' was built under R version 4.3.1Warning: package 'dials' was built under R version 4.3.1Warning: package 'scales' was built under R version 4.3.1Warning: package 'infer' was built under R version 4.3.1Warning: package 'modeldata' was built under R version 4.3.1Warning: package 'parsnip' was built under R version 4.3.1Warning: package 'recipes' was built under R version 4.3.1Warning: package 'rsample' was built under R version 4.3.1Warning: package 'tune' was built under R version 4.3.1Warning: package 'workflows' was built under R version 4.3.1Warning: package 'workflowsets' was built under R version 4.3.1Warning: package 'yardstick' was built under R version 4.3.1── Conflicts ───────────────────────────────────────── tidymodels_conflicts() ──
✖ scales::discard() masks purrr::discard()
✖ tidyr::extract() masks magrittr::extract()
✖ dplyr::filter() masks stats::filter()
✖ recipes::fixed() masks stringr::fixed()
✖ dplyr::lag() masks stats::lag()
✖ purrr::set_names() masks magrittr::set_names()
✖ yardstick::spec() masks readr::spec()
✖ recipes::step() masks stats::step()
• Dig deeper into tidy modeling with R at https://www.tmwr.orglibrary(gt) # for making display tablesWarning: package 'gt' was built under R version 4.3.1library(gtExtras) # helper functions for beautiful tablesWarning: package 'gtExtras' was built under R version 4.3.1library(DataExplorer) #Warning: package 'DataExplorer' was built under R version 4.3.1Exercise 1
view(the_tate)
view(the_tate_artists)the_tate %>% dplyr::summarize(
no_artists = n_distinct(artistId),
max_period_year = max(year, na.rm = TRUE),
min_period_year = min(year, na.rm = TRUE),
max_period_acquisitionYear = max(acquisitionYear, na.rm = TRUE),
min_period_acquisitionYear = min(acquisitionYear, na.rm = TRUE),
)# A tibble: 1 × 5
no_artists max_period_year min_period_year max_period_acquisitionYear
<int> <dbl> <dbl> <dbl>
1 3342 2012 1545 2013
# ℹ 1 more variable: min_period_acquisitionYear <dbl>the_tate %>% DataExplorer::introduce() # A tibble: 1 × 9
rows columns discrete_columns continuous_columns all_missing_columns
<int> <int> <int> <int> <int>
1 69201 20 13 7 0
# ℹ 4 more variables: total_missing_values <int>, complete_rows <int>,
# total_observations <int>, memory_usage <dbl>the_tate %>% DataExplorer::plot_missing()
The the_tate dataset has 3342 unique artists who worked from 1545 to 2012. The works were acquired between the years 1823 and 2013 .
Exercise 2
ct <- the_tate %>% dplyr::select(artistId,title) %>% dplyr::filter(title %in% c("[no title]","Untitled","Blank"))
table(ct) title
artistId [no title] Blank Untitled
558 0 3031 0
622 16 0 0
628 0 0 2
639 2 0 0
650 0 0 2
653 0 0 1
654 1 0 1
680 0 0 1
686 1 0 0
687 10 0 0
699 50 0 2
715 1 0 0
727 0 0 4
732 0 0 14
745 0 0 1
746 1 0 1
747 3 0 21
757 0 0 1
770 0 0 1
776 0 0 1
784 13 0 0
785 0 0 2
798 0 0 2
801 1 0 0
805 15 0 0
806 0 0 1
813 1 0 1
827 13 0 1
828 21 0 0
834 9 0 0
848 0 0 1
855 0 0 6
873 1 0 0
878 0 0 1
880 0 0 1
887 0 0 1
891 10 0 0
917 10 0 0
921 0 0 1
924 0 0 6
925 9 0 7
930 0 0 2
937 1 0 0
944 0 0 1
945 1 0 0
951 0 0 4
965 0 0 1
986 12 0 0
997 35 0 1
1009 10 0 0
1011 9 0 3
1023 1 0 0
1030 0 0 1
1067 0 0 1
1072 0 0 6
1093 7 0 0
1095 0 0 1
1096 0 0 1
1098 5 0 0
1100 0 0 1
1114 9 0 0
1116 0 0 33
1126 0 0 1
1137 32 0 4
1165 0 0 6
1198 0 0 1
1203 0 0 1
1210 1 0 0
1222 1 0 0
1231 0 0 13
1244 2 0 0
1249 2 0 0
1257 0 0 1
1270 0 0 1
1274 0 0 1
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1289 0 0 6
1291 0 0 1
1295 0 0 2
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1312 26 0 0
1314 5 0 0
1315 0 0 1
1318 0 0 1
1355 0 0 1
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1378 32 0 7
1384 22 0 15
1387 0 0 1
1391 4 0 1
1406 0 0 2
1407 2 0 0
1416 14 0 2
1430 11 0 0
1433 0 0 2
1438 12 0 11
1447 0 0 1
1448 1 0 2
1451 0 0 1
1455 1 0 0
1466 0 0 1
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1494 0 0 1
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1504 76 0 2
1512 10 0 3
1523 6 0 0
1525 3 0 2
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1546 0 0 3
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1578 20 0 1
1585 0 0 1
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1615 0 0 1
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1635 1 0 0
1646 0 0 1
1657 0 0 1
1669 0 0 2
1673 1 0 0
1679 0 0 1
1683 13 0 0
1685 0 0 1
1691 0 0 3
1738 135 0 0
1742 0 0 1
1744 16 0 1
1754 11 0 0
1763 0 0 3
1764 23 0 0
1772 0 0 3
1774 25 0 0
1786 0 0 1
1788 1 0 0
1792 0 0 4
1798 0 0 1
1826 1 0 0
1838 0 0 2
1839 0 0 2
1841 0 0 1
1843 4 0 0
1845 0 0 1
1870 8 0 1
1875 0 0 3
1888 7 0 0
1892 0 0 2
1895 0 0 1
1897 4 0 0
1900 1 0 0
1913 0 0 1
1917 5 0 0
1922 12 0 0
1933 0 0 1
1934 0 0 3
1938 0 0 15
1955 0 0 1
1959 7 0 3
1968 1 0 0
1998 1 0 0
2000 0 0 2
2004 2 0 0
2005 6 0 1
2007 0 0 2
2023 0 0 1
2042 7 0 0
2043 34 0 0
2045 1 0 0
2065 7 0 0
2066 12 0 1
2073 15 0 1
2075 0 0 2
2081 30 0 4
2095 0 0 2
2098 1 0 0
2101 0 0 2
2116 39 0 33
2121 30 0 0
2126 0 0 2
2130 0 0 2
2131 1 0 0
2146 4 0 2
2154 34 0 1
2155 26 0 1
2161 0 0 1
2164 33 0 0
2170 5 0 0
2174 1 0 0
2177 1 0 1
2196 6 0 0
2201 10 0 0
2203 11 0 9
2205 2 0 2
2220 0 0 1
2234 2 0 0
2235 1 0 0
2236 0 0 1
2237 1 0 0
2238 48 0 1
2239 0 0 1
2240 0 0 1
2253 1 0 0
2257 1 0 0
2258 0 0 1
2260 12 0 0
2264 0 0 1
2269 0 0 5
2277 0 0 1
2278 0 0 1
2280 0 0 1
2293 0 0 1
2308 0 0 1
2309 0 0 4
2311 0 0 3
2312 8 0 0
2319 0 0 1
2335 15 0 0
2347 0 0 1
2361 8 0 9
2371 0 0 1
2374 152 0 0
2380 1 0 0
2398 10 0 0
2402 15 0 0
2403 1 0 0
2543 1 0 1
2586 1 0 0
2587 1 0 0
2588 1 0 1
2589 1 0 0
2590 1 0 0
2591 1 0 1
2592 1 0 0
2593 1 0 0
2594 1 0 0
2595 1 0 0
2596 1 0 0
2597 1 0 0
2598 0 0 1
2600 8 0 0
2612 8 0 5
2656 0 0 1
2659 0 0 1
2669 25 0 0
2677 0 0 5
2678 10 0 0
2685 12 0 0
2695 0 0 2
2697 6 0 0
2705 7 0 0
2730 0 0 1
2749 0 0 1
2752 0 0 2
2757 0 0 4
2759 0 0 1
2764 0 0 1
2771 1 0 0
2784 0 0 8
3099 8 0 0
3246 8 0 0
4427 0 0 2
4531 0 0 1
4731 0 0 4
4831 0 0 1
5755 0 0 5
6003 0 0 1
6237 0 0 4
6673 21 0 0
6858 30 0 0
6860 0 0 11
6872 8 0 0
7077 0 0 1
7255 0 0 7
7334 0 0 1
7467 2 0 7
7630 0 0 1
7640 0 0 3
8143 0 0 1
8314 0 0 2
8784 0 0 1
9553 0 0 1
9560 1 0 0
9636 0 0 1
9936 0 0 30
10009 0 0 6
10068 3 0 0
10168 0 0 1
10169 0 0 1
10208 0 0 11
10429 0 0 1
10512 0 0 11
10609 0 0 1
10610 0 0 2
10611 0 0 3
10613 125 0 1
10844 0 0 5
10908 0 0 16
11360 0 0 10
11551 0 0 1
11698 0 0 2
11852 0 0 2
12525 0 0 2
13288 0 0 2
13424 0 0 1
13793 0 0 1
14424 0 0 2
14527 0 0 1
14743 0 0 1
15525 0 0 2
15549 0 0 4
16340 0 0 1
16467 0 0 1
16658 0 0 1
16988 0 0 1table(the_tate$id,the_tate$year,useNA = "ifany")
1545 1557 1563 1565 1569 1573 1576 1586 1592 1594 1595 1596 1600 1605
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2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 <NA>
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256 0 0 0 0 0 0 0 0 0 0 0
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260 0 0 0 0 0 0 0 0 0 0 0
261 0 0 0 0 0 0 0 0 0 0 0
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280 0 0 0 0 0 0 0 0 0 0 0
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284 0 0 0 0 0 0 0 0 0 0 0
285 0 0 0 0 0 0 0 0 0 0 0
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310 0 0 0 0 0 0 0 0 0 0 0
311 0 0 0 0 0 0 0 0 0 0 0
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314 0 0 0 0 0 0 0 0 0 0 0
315 0 0 0 0 0 0 0 0 0 0 0
316 0 0 0 0 0 0 0 0 0 0 0
317 0 0 0 0 0 0 0 0 0 0 1
318 0 0 0 0 0 0 0 0 0 0 1
319 0 0 0 0 0 0 0 0 0 0 0
320 0 0 0 0 0 0 0 0 0 0 0
321 0 0 0 0 0 0 0 0 0 0 0
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325 0 0 0 0 0 0 0 0 0 0 0
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330 0 0 0 0 0 0 0 0 0 0 0
331 0 0 0 0 0 0 0 0 0 0 0
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333 0 0 0 0 0 0 0 0 0 0 0
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336 0 0 0 0 0 0 0 0 0 0 0
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345 0 0 0 0 0 0 0 0 0 0 0
346 0 0 0 0 0 0 0 0 0 0 0
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371 0 0 0 0 0 0 0 0 0 0 0
372 0 0 0 0 0 0 0 0 0 0 0
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376 0 0 0 0 0 0 0 0 0 0 0
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382 0 0 0 0 0 0 0 0 0 0 0
383 0 0 0 0 0 0 0 0 0 0 0
384 0 0 0 0 0 0 0 0 0 0 0
385 0 0 0 0 0 0 0 0 0 0 0
386 0 0 0 0 0 0 0 0 0 0 0
387 0 0 0 0 0 0 0 0 0 0 0
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389 0 0 0 0 0 0 0 0 0 0 0
390 0 0 0 0 0 0 0 0 0 0 0
391 0 0 0 0 0 0 0 0 0 0 0
392 0 0 0 0 0 0 0 0 0 0 0
393 0 0 0 0 0 0 0 0 0 0 0
394 0 0 0 0 0 0 0 0 0 0 0
395 0 0 0 0 0 0 0 0 0 0 0
396 0 0 0 0 0 0 0 0 0 0 0
397 0 0 0 0 0 0 0 0 0 0 0
398 0 0 0 0 0 0 0 0 0 0 0
399 0 0 0 0 0 0 0 0 0 0 0
400 0 0 0 0 0 0 0 0 0 0 0
401 0 0 0 0 0 0 0 0 0 0 0
402 0 0 0 0 0 0 0 0 0 0 0
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406 0 0 0 0 0 0 0 0 0 0 0
[ reached getOption("max.print") -- omitted 68924 rows ]#— Number of records with missing dates —
ct3 <- sum(is.na(the_tate$year))
ct4 <- the_tate %>% dplyr::select(artistId , year) %>% dplyr::filter(is.na(year))
artists_with_missing_years <- ct4 %>% dplyr::group_by(artistId) %>% dplyr::summarize(
missing_no = n()
) %>% dplyr::arrange(desc(missing_no))
artists_with_missing_years <- artists_with_missing_years %>% dplyr::mutate(pct_missing_years = (missing_no/sum(missing_no))*100,cumsum(pct_missing_years))
count(distinct(ct4,artistId))# A tibble: 1 × 1
n
<int>
1 462count(ct4)# A tibble: 1 × 1
n
<int>
1 5397How number of works with missing dates is 5397.
The number of artists whose works have missing dates is 462.
It would require resolving missing year data for only 11 artists resolve resolve at least 50% of the missing data.
The missing year data likely to be classified as MAR.
Exercise 3
artist_works <- the_tate %>% dplyr::group_by(artistId) %>% dplyr::summarize(
number_of_works = n()
) %>% dplyr::arrange(desc(number_of_works))
artist_works <- artist_works %>% dplyr::mutate(pct_of_work = (number_of_works/sum(number_of_works))*100)
artist_works %>% gt() %>%
gt_theme_538() | artistId | number_of_works | pct_of_work |
|---|---|---|
| 558 | 39389 | 56.919697692 |
| 300 | 1046 | 1.511538851 |
| 1659 | 623 | 0.900276008 |
| 138 | 612 | 0.884380284 |
| 747 | 578 | 0.835248046 |
| 2638 | 388 | 0.560685539 |
| 1738 | 385 | 0.556350342 |
| 186 | 287 | 0.414733891 |
| 1764 | 274 | 0.395948035 |
| 2121 | 272 | 0.393057904 |
| 108 | 249 | 0.359821390 |
| 118 | 237 | 0.342480600 |
| 531 | 215 | 0.310689152 |
| 10613 | 199 | 0.287568099 |
| 1774 | 183 | 0.264447046 |
| 39 | 180 | 0.260111848 |
| 1416 | 179 | 0.258666782 |
| 136 | 169 | 0.244216124 |
| 1093 | 164 | 0.236990795 |
| 1100 | 162 | 0.234100663 |
| 199 | 158 | 0.228320400 |
| 2374 | 156 | 0.225430268 |
| 2043 | 152 | 0.219650005 |
| 1855 | 142 | 0.205199347 |
| 68 | 138 | 0.199419084 |
| 1244 | 138 | 0.199419084 |
| 1708 | 135 | 0.195083886 |
| 1744 | 135 | 0.195083886 |
| 2116 | 135 | 0.195083886 |
| 666 | 133 | 0.192193754 |
| 1137 | 132 | 0.190748689 |
| 1168 | 128 | 0.184968425 |
| 1124 | 125 | 0.180633228 |
| 873 | 124 | 0.179188162 |
| 1274 | 123 | 0.177743096 |
| 2154 | 122 | 0.176298030 |
| 11598 | 119 | 0.171962833 |
| 1436 | 116 | 0.167627635 |
| 1293 | 111 | 0.160402306 |
| 1312 | 110 | 0.158957241 |
| 20 | 109 | 0.157512175 |
| 6711 | 109 | 0.157512175 |
| 622 | 108 | 0.156067109 |
| 2065 | 105 | 0.151731911 |
| 140 | 104 | 0.150286846 |
| 569 | 102 | 0.147396714 |
| 1959 | 96 | 0.138726319 |
| 211 | 94 | 0.135836187 |
| 1504 | 94 | 0.135836187 |
| 2081 | 93 | 0.134391122 |
| 116 | 92 | 0.132946056 |
| 1278 | 92 | 0.132946056 |
| 145 | 91 | 0.131500990 |
| 1836 | 89 | 0.128610858 |
| 78 | 87 | 0.125720727 |
| 123 | 85 | 0.122830595 |
| 997 | 85 | 0.122830595 |
| 518 | 84 | 0.121385529 |
| 59 | 83 | 0.119940463 |
| 391 | 82 | 0.118495397 |
| 286 | 81 | 0.117050332 |
| 1702 | 80 | 0.115605266 |
| 256 | 79 | 0.114160200 |
| 676 | 76 | 0.109825003 |
| 1922 | 76 | 0.109825003 |
| 2155 | 76 | 0.109825003 |
| 2284 | 76 | 0.109825003 |
| 930 | 75 | 0.108379937 |
| 11413 | 75 | 0.108379937 |
| 1673 | 74 | 0.106934871 |
| 351 | 72 | 0.104044739 |
| 2075 | 69 | 0.099709542 |
| 5271 | 69 | 0.099709542 |
| 699 | 68 | 0.098264476 |
| 1295 | 68 | 0.098264476 |
| 2441 | 68 | 0.098264476 |
| 606 | 66 | 0.095374344 |
| 1994 | 66 | 0.095374344 |
| 1481 | 65 | 0.093929278 |
| 379 | 64 | 0.092484213 |
| 1578 | 64 | 0.092484213 |
| 2559 | 64 | 0.092484213 |
| 1977 | 63 | 0.091039147 |
| 2565 | 63 | 0.091039147 |
| 2747 | 63 | 0.091039147 |
| 29 | 62 | 0.089594081 |
| 1518 | 62 | 0.089594081 |
| 117 | 60 | 0.086703949 |
| 600 | 60 | 0.086703949 |
| 1143 | 60 | 0.086703949 |
| 1870 | 60 | 0.086703949 |
| 2555 | 60 | 0.086703949 |
| 6673 | 60 | 0.086703949 |
| 1368 | 59 | 0.085258884 |
| 1512 | 59 | 0.085258884 |
| 1188 | 56 | 0.080923686 |
| 2238 | 56 | 0.080923686 |
| 461 | 55 | 0.079478620 |
| 2014 | 55 | 0.079478620 |
| 2576 | 55 | 0.079478620 |
| 304 | 54 | 0.078033554 |
| 1116 | 54 | 0.078033554 |
| 2308 | 54 | 0.078033554 |
| 925 | 52 | 0.075143423 |
| 1126 | 51 | 0.073698357 |
| 682 | 50 | 0.072253291 |
| 1941 | 50 | 0.072253291 |
| 2480 | 50 | 0.072253291 |
| 60 | 49 | 0.070808225 |
| 148 | 49 | 0.070808225 |
| 1384 | 49 | 0.070808225 |
| 924 | 48 | 0.069363159 |
| 1525 | 48 | 0.069363159 |
| 1916 | 47 | 0.067918094 |
| 2259 | 47 | 0.067918094 |
| 143 | 46 | 0.066473028 |
| 265 | 46 | 0.066473028 |
| 1148 | 46 | 0.066473028 |
| 1823 | 46 | 0.066473028 |
| 7026 | 46 | 0.066473028 |
| 1231 | 45 | 0.065027962 |
| 1585 | 45 | 0.065027962 |
| 15501 | 45 | 0.065027962 |
| 475 | 44 | 0.063582896 |
| 586 | 44 | 0.063582896 |
| 777 | 44 | 0.063582896 |
| 1873 | 43 | 0.062137830 |
| 1874 | 43 | 0.062137830 |
| 1009 | 42 | 0.060692765 |
| 1362 | 42 | 0.060692765 |
| 1767 | 42 | 0.060692765 |
| 2269 | 42 | 0.060692765 |
| 11595 | 42 | 0.060692765 |
| 293 | 41 | 0.059247699 |
| 444 | 41 | 0.059247699 |
| 1378 | 41 | 0.059247699 |
| 1380 | 41 | 0.059247699 |
| 1691 | 41 | 0.059247699 |
| 2335 | 41 | 0.059247699 |
| 2361 | 41 | 0.059247699 |
| 278 | 40 | 0.057802633 |
| 787 | 40 | 0.057802633 |
| 1187 | 40 | 0.057802633 |
| 1917 | 40 | 0.057802633 |
| 65 | 39 | 0.056357567 |
| 1307 | 39 | 0.056357567 |
| 1318 | 39 | 0.056357567 |
| 1478 | 39 | 0.056357567 |
| 12989 | 39 | 0.056357567 |
| 24 | 38 | 0.054912501 |
| 368 | 38 | 0.054912501 |
| 508 | 38 | 0.054912501 |
| 553 | 38 | 0.054912501 |
| 1114 | 38 | 0.054912501 |
| 1777 | 38 | 0.054912501 |
| 1990 | 38 | 0.054912501 |
| 2170 | 38 | 0.054912501 |
| 2073 | 37 | 0.053467435 |
| 92 | 36 | 0.052022370 |
| 341 | 36 | 0.052022370 |
| 463 | 36 | 0.052022370 |
| 9936 | 36 | 0.052022370 |
| 159 | 35 | 0.050577304 |
| 492 | 35 | 0.050577304 |
| 763 | 35 | 0.050577304 |
| 986 | 35 | 0.050577304 |
| 1315 | 35 | 0.050577304 |
| 1508 | 35 | 0.050577304 |
| 1882 | 35 | 0.050577304 |
| 2317 | 35 | 0.050577304 |
| 2731 | 35 | 0.050577304 |
| 828 | 34 | 0.049132238 |
| 1133 | 34 | 0.049132238 |
| 1730 | 34 | 0.049132238 |
| 2164 | 34 | 0.049132238 |
| 2669 | 34 | 0.049132238 |
| 6500 | 34 | 0.049132238 |
| 525 | 33 | 0.047687172 |
| 1276 | 33 | 0.047687172 |
| 1852 | 33 | 0.047687172 |
| 1438 | 32 | 0.046242106 |
| 1365 | 31 | 0.044797041 |
| 1430 | 31 | 0.044797041 |
| 1763 | 31 | 0.044797041 |
| 1845 | 31 | 0.044797041 |
| 2146 | 31 | 0.044797041 |
| 2416 | 31 | 0.044797041 |
| 2675 | 31 | 0.044797041 |
| 554 | 30 | 0.043351975 |
| 697 | 30 | 0.043351975 |
| 732 | 30 | 0.043351975 |
| 1690 | 30 | 0.043351975 |
| 1938 | 30 | 0.043351975 |
| 2319 | 30 | 0.043351975 |
| 2591 | 30 | 0.043351975 |
| 6858 | 30 | 0.043351975 |
| 15975 | 30 | 0.043351975 |
| 337 | 29 | 0.041906909 |
| 921 | 29 | 0.041906909 |
| 1499 | 29 | 0.041906909 |
| 1725 | 29 | 0.041906909 |
| 2351 | 29 | 0.041906909 |
| 2643 | 29 | 0.041906909 |
| 6633 | 29 | 0.041906909 |
| 15855 | 29 | 0.041906909 |
| 50 | 28 | 0.040461843 |
| 79 | 28 | 0.040461843 |
| 722 | 28 | 0.040461843 |
| 778 | 28 | 0.040461843 |
| 1203 | 28 | 0.040461843 |
| 1703 | 28 | 0.040461843 |
| 342 | 27 | 0.039016777 |
| 350 | 27 | 0.039016777 |
| 392 | 27 | 0.039016777 |
| 880 | 27 | 0.039016777 |
| 1212 | 27 | 0.039016777 |
| 1426 | 27 | 0.039016777 |
| 2523 | 27 | 0.039016777 |
| 457 | 26 | 0.037571711 |
| 581 | 26 | 0.037571711 |
| 1120 | 26 | 0.037571711 |
| 2279 | 26 | 0.037571711 |
| 2423 | 26 | 0.037571711 |
| 2590 | 26 | 0.037571711 |
| 2688 | 26 | 0.037571711 |
| 5275 | 26 | 0.037571711 |
| 7743 | 26 | 0.037571711 |
| 389 | 25 | 0.036126646 |
| 979 | 25 | 0.036126646 |
| 1061 | 25 | 0.036126646 |
| 1163 | 25 | 0.036126646 |
| 1406 | 25 | 0.036126646 |
| 1462 | 25 | 0.036126646 |
| 1721 | 25 | 0.036126646 |
| 2203 | 25 | 0.036126646 |
| 2614 | 25 | 0.036126646 |
| 6550 | 25 | 0.036126646 |
| 323 | 24 | 0.034681580 |
| 1367 | 24 | 0.034681580 |
| 1386 | 24 | 0.034681580 |
| 1502 | 24 | 0.034681580 |
| 2790 | 24 | 0.034681580 |
| 57 | 23 | 0.033236514 |
| 538 | 23 | 0.033236514 |
| 707 | 23 | 0.033236514 |
| 784 | 23 | 0.033236514 |
| 1533 | 23 | 0.033236514 |
| 1656 | 23 | 0.033236514 |
| 1699 | 23 | 0.033236514 |
| 2002 | 23 | 0.033236514 |
| 2222 | 23 | 0.033236514 |
| 2403 | 23 | 0.033236514 |
| 6461 | 23 | 0.033236514 |
| 16115 | 23 | 0.033236514 |
| 172 | 22 | 0.031791448 |
| 480 | 22 | 0.031791448 |
| 636 | 22 | 0.031791448 |
| 781 | 22 | 0.031791448 |
| 914 | 22 | 0.031791448 |
| 955 | 22 | 0.031791448 |
| 1222 | 22 | 0.031791448 |
| 1259 | 22 | 0.031791448 |
| 1467 | 22 | 0.031791448 |
| 1654 | 22 | 0.031791448 |
| 1674 | 22 | 0.031791448 |
| 1794 | 22 | 0.031791448 |
| 1813 | 22 | 0.031791448 |
| 2130 | 22 | 0.031791448 |
| 2788 | 22 | 0.031791448 |
| 9074 | 22 | 0.031791448 |
| 176 | 21 | 0.030346382 |
| 411 | 21 | 0.030346382 |
| 427 | 21 | 0.030346382 |
| 805 | 21 | 0.030346382 |
| 827 | 21 | 0.030346382 |
| 1159 | 21 | 0.030346382 |
| 1291 | 21 | 0.030346382 |
| 1391 | 21 | 0.030346382 |
| 1464 | 21 | 0.030346382 |
| 1476 | 21 | 0.030346382 |
| 1610 | 21 | 0.030346382 |
| 1689 | 21 | 0.030346382 |
| 1841 | 21 | 0.030346382 |
| 1866 | 21 | 0.030346382 |
| 2358 | 21 | 0.030346382 |
| 2368 | 21 | 0.030346382 |
| 2371 | 21 | 0.030346382 |
| 3038 | 21 | 0.030346382 |
| 13509 | 21 | 0.030346382 |
| 1559 | 20 | 0.028901316 |
| 1837 | 20 | 0.028901316 |
| 2680 | 20 | 0.028901316 |
| 10345 | 20 | 0.028901316 |
| 346 | 19 | 0.027456251 |
| 539 | 19 | 0.027456251 |
| 865 | 19 | 0.027456251 |
| 917 | 19 | 0.027456251 |
| 934 | 19 | 0.027456251 |
| 1035 | 19 | 0.027456251 |
| 1210 | 19 | 0.027456251 |
| 1470 | 19 | 0.027456251 |
| 1593 | 19 | 0.027456251 |
| 1815 | 19 | 0.027456251 |
| 2372 | 19 | 0.027456251 |
| 2402 | 19 | 0.027456251 |
| 6664 | 19 | 0.027456251 |
| 81 | 18 | 0.026011185 |
| 105 | 18 | 0.026011185 |
| 287 | 18 | 0.026011185 |
| 334 | 18 | 0.026011185 |
| 503 | 18 | 0.026011185 |
| 837 | 18 | 0.026011185 |
| 1190 | 18 | 0.026011185 |
| 1242 | 18 | 0.026011185 |
| 1289 | 18 | 0.026011185 |
| 1638 | 18 | 0.026011185 |
| 1683 | 18 | 0.026011185 |
| 1697 | 18 | 0.026011185 |
| 1998 | 18 | 0.026011185 |
| 2079 | 18 | 0.026011185 |
| 2142 | 18 | 0.026011185 |
| 2339 | 18 | 0.026011185 |
| 2648 | 18 | 0.026011185 |
| 10512 | 18 | 0.026011185 |
| 13142 | 18 | 0.026011185 |
| 96 | 17 | 0.024566119 |
| 328 | 17 | 0.024566119 |
| 397 | 17 | 0.024566119 |
| 546 | 17 | 0.024566119 |
| 628 | 17 | 0.024566119 |
| 844 | 17 | 0.024566119 |
| 1129 | 17 | 0.024566119 |
| 1257 | 17 | 0.024566119 |
| 1268 | 17 | 0.024566119 |
| 1692 | 17 | 0.024566119 |
| 1754 | 17 | 0.024566119 |
| 1772 | 17 | 0.024566119 |
| 1897 | 17 | 0.024566119 |
| 2386 | 17 | 0.024566119 |
| 2408 | 17 | 0.024566119 |
| 2543 | 17 | 0.024566119 |
| 10908 | 17 | 0.024566119 |
| 119 | 16 | 0.023121053 |
| 268 | 16 | 0.023121053 |
| 433 | 16 | 0.023121053 |
| 575 | 16 | 0.023121053 |
| 659 | 16 | 0.023121053 |
| 1014 | 16 | 0.023121053 |
| 1255 | 16 | 0.023121053 |
| 1724 | 16 | 0.023121053 |
| 1912 | 16 | 0.023121053 |
| 1995 | 16 | 0.023121053 |
| 2103 | 16 | 0.023121053 |
| 2147 | 16 | 0.023121053 |
| 2220 | 16 | 0.023121053 |
| 2230 | 16 | 0.023121053 |
| 2312 | 16 | 0.023121053 |
| 2409 | 16 | 0.023121053 |
| 7467 | 16 | 0.023121053 |
| 10208 | 16 | 0.023121053 |
| 15957 | 16 | 0.023121053 |
| 276 | 15 | 0.021675987 |
| 446 | 15 | 0.021675987 |
| 502 | 15 | 0.021675987 |
| 680 | 15 | 0.021675987 |
| 730 | 15 | 0.021675987 |
| 816 | 15 | 0.021675987 |
| 891 | 15 | 0.021675987 |
| 1066 | 15 | 0.021675987 |
| 1314 | 15 | 0.021675987 |
| 1399 | 15 | 0.021675987 |
| 1605 | 15 | 0.021675987 |
| 1665 | 15 | 0.021675987 |
| 1839 | 15 | 0.021675987 |
| 2042 | 15 | 0.021675987 |
| 2253 | 15 | 0.021675987 |
| 2260 | 15 | 0.021675987 |
| 2534 | 15 | 0.021675987 |
| 2612 | 15 | 0.021675987 |
| 2685 | 15 | 0.021675987 |
| 6872 | 15 | 0.021675987 |
| 7810 | 15 | 0.021675987 |
| 10184 | 15 | 0.021675987 |
| 41 | 14 | 0.020230922 |
| 283 | 14 | 0.020230922 |
| 371 | 14 | 0.020230922 |
| 550 | 14 | 0.020230922 |
| 594 | 14 | 0.020230922 |
| 664 | 14 | 0.020230922 |
| 737 | 14 | 0.020230922 |
| 803 | 14 | 0.020230922 |
| 951 | 14 | 0.020230922 |
| 1221 | 14 | 0.020230922 |
| 1345 | 14 | 0.020230922 |
| 1363 | 14 | 0.020230922 |
| 1603 | 14 | 0.020230922 |
| 1615 | 14 | 0.020230922 |
| 1629 | 14 | 0.020230922 |
| 1646 | 14 | 0.020230922 |
| 1698 | 14 | 0.020230922 |
| 1843 | 14 | 0.020230922 |
| 1919 | 14 | 0.020230922 |
| 1958 | 14 | 0.020230922 |
| 2115 | 14 | 0.020230922 |
| 2307 | 14 | 0.020230922 |
| 2337 | 14 | 0.020230922 |
| 2517 | 14 | 0.020230922 |
| 2789 | 14 | 0.020230922 |
| 5975 | 14 | 0.020230922 |
| 6275 | 14 | 0.020230922 |
| 8795 | 14 | 0.020230922 |
| 9937 | 14 | 0.020230922 |
| 14410 | 14 | 0.020230922 |
| 17198 | 14 | 0.020230922 |
| 126 | 13 | 0.018785856 |
| 412 | 13 | 0.018785856 |
| 435 | 13 | 0.018785856 |
| 471 | 13 | 0.018785856 |
| 568 | 13 | 0.018785856 |
| 615 | 13 | 0.018785856 |
| 650 | 13 | 0.018785856 |
| 687 | 13 | 0.018785856 |
| 711 | 13 | 0.018785856 |
| 776 | 13 | 0.018785856 |
| 815 | 13 | 0.018785856 |
| 927 | 13 | 0.018785856 |
| 953 | 13 | 0.018785856 |
| 985 | 13 | 0.018785856 |
| 988 | 13 | 0.018785856 |
| 1084 | 13 | 0.018785856 |
| 1156 | 13 | 0.018785856 |
| 1370 | 13 | 0.018785856 |
| 1573 | 13 | 0.018785856 |
| 1604 | 13 | 0.018785856 |
| 1875 | 13 | 0.018785856 |
| 1901 | 13 | 0.018785856 |
| 2000 | 13 | 0.018785856 |
| 2066 | 13 | 0.018785856 |
| 2113 | 13 | 0.018785856 |
| 2168 | 13 | 0.018785856 |
| 2364 | 13 | 0.018785856 |
| 2599 | 13 | 0.018785856 |
| 2709 | 13 | 0.018785856 |
| 2760 | 13 | 0.018785856 |
| 4427 | 13 | 0.018785856 |
| 10836 | 13 | 0.018785856 |
| 11957 | 13 | 0.018785856 |
| 14992 | 13 | 0.018785856 |
| 198 | 12 | 0.017340790 |
| 208 | 12 | 0.017340790 |
| 447 | 12 | 0.017340790 |
| 488 | 12 | 0.017340790 |
| 577 | 12 | 0.017340790 |
| 668 | 12 | 0.017340790 |
| 706 | 12 | 0.017340790 |
| 834 | 12 | 0.017340790 |
| 1011 | 12 | 0.017340790 |
| 1211 | 12 | 0.017340790 |
| 1305 | 12 | 0.017340790 |
| 1350 | 12 | 0.017340790 |
| 1488 | 12 | 0.017340790 |
| 1513 | 12 | 0.017340790 |
| 1563 | 12 | 0.017340790 |
| 1915 | 12 | 0.017340790 |
| 2055 | 12 | 0.017340790 |
| 2056 | 12 | 0.017340790 |
| 2096 | 12 | 0.017340790 |
| 2198 | 12 | 0.017340790 |
| 2295 | 12 | 0.017340790 |
| 2360 | 12 | 0.017340790 |
| 2389 | 12 | 0.017340790 |
| 2476 | 12 | 0.017340790 |
| 2585 | 12 | 0.017340790 |
| 2678 | 12 | 0.017340790 |
| 2785 | 12 | 0.017340790 |
| 6860 | 12 | 0.017340790 |
| 8402 | 12 | 0.017340790 |
| 11249 | 12 | 0.017340790 |
| 15851 | 12 | 0.017340790 |
| 16107 | 12 | 0.017340790 |
| 87 | 11 | 0.015895724 |
| 301 | 11 | 0.015895724 |
| 349 | 11 | 0.015895724 |
| 385 | 11 | 0.015895724 |
| 388 | 11 | 0.015895724 |
| 513 | 11 | 0.015895724 |
| 598 | 11 | 0.015895724 |
| 613 | 11 | 0.015895724 |
| 620 | 11 | 0.015895724 |
| 681 | 11 | 0.015895724 |
| 717 | 11 | 0.015895724 |
| 731 | 11 | 0.015895724 |
| 842 | 11 | 0.015895724 |
| 877 | 11 | 0.015895724 |
| 1172 | 11 | 0.015895724 |
| 1175 | 11 | 0.015895724 |
| 1277 | 11 | 0.015895724 |
| 1284 | 11 | 0.015895724 |
| 1290 | 11 | 0.015895724 |
| 1405 | 11 | 0.015895724 |
| 1480 | 11 | 0.015895724 |
| 1519 | 11 | 0.015895724 |
| 1590 | 11 | 0.015895724 |
| 1667 | 11 | 0.015895724 |
| 1685 | 11 | 0.015895724 |
| 1800 | 11 | 0.015895724 |
| 1935 | 11 | 0.015895724 |
| 1956 | 11 | 0.015895724 |
| 2005 | 11 | 0.015895724 |
| 2108 | 11 | 0.015895724 |
| 2398 | 11 | 0.015895724 |
| 2419 | 11 | 0.015895724 |
| 2460 | 11 | 0.015895724 |
| 2600 | 11 | 0.015895724 |
| 2677 | 11 | 0.015895724 |
| 3099 | 11 | 0.015895724 |
| 4779 | 11 | 0.015895724 |
| 5905 | 11 | 0.015895724 |
| 7945 | 11 | 0.015895724 |
| 11360 | 11 | 0.015895724 |
| 11979 | 11 | 0.015895724 |
| 260 | 10 | 0.014450658 |
| 426 | 10 | 0.014450658 |
| 534 | 10 | 0.014450658 |
| 648 | 10 | 0.014450658 |
| 671 | 10 | 0.014450658 |
| 785 | 10 | 0.014450658 |
| 796 | 10 | 0.014450658 |
| 912 | 10 | 0.014450658 |
| 926 | 10 | 0.014450658 |
| 963 | 10 | 0.014450658 |
| 1008 | 10 | 0.014450658 |
| 1018 | 10 | 0.014450658 |
| 1036 | 10 | 0.014450658 |
| 1072 | 10 | 0.014450658 |
| 1073 | 10 | 0.014450658 |
| 1336 | 10 | 0.014450658 |
| 1456 | 10 | 0.014450658 |
| 1616 | 10 | 0.014450658 |
| 1681 | 10 | 0.014450658 |
| 1688 | 10 | 0.014450658 |
| 1769 | 10 | 0.014450658 |
| 1872 | 10 | 0.014450658 |
| 1888 | 10 | 0.014450658 |
| 2127 | 10 | 0.014450658 |
| 2157 | 10 | 0.014450658 |
| 2201 | 10 | 0.014450658 |
| 2365 | 10 | 0.014450658 |
| 2378 | 10 | 0.014450658 |
| 2407 | 10 | 0.014450658 |
| 2436 | 10 | 0.014450658 |
| 2469 | 10 | 0.014450658 |
| 2496 | 10 | 0.014450658 |
| 2498 | 10 | 0.014450658 |
| 8297 | 10 | 0.014450658 |
| 10761 | 10 | 0.014450658 |
| 14400 | 10 | 0.014450658 |
| 14941 | 10 | 0.014450658 |
| 16030 | 10 | 0.014450658 |
| 16033 | 10 | 0.014450658 |
| 16113 | 10 | 0.014450658 |
| 164 | 9 | 0.013005592 |
| 167 | 9 | 0.013005592 |
| 230 | 9 | 0.013005592 |
| 242 | 9 | 0.013005592 |
| 247 | 9 | 0.013005592 |
| 261 | 9 | 0.013005592 |
| 406 | 9 | 0.013005592 |
| 437 | 9 | 0.013005592 |
| 473 | 9 | 0.013005592 |
| 595 | 9 | 0.013005592 |
| 661 | 9 | 0.013005592 |
| 667 | 9 | 0.013005592 |
| 749 | 9 | 0.013005592 |
| 904 | 9 | 0.013005592 |
| 1038 | 9 | 0.013005592 |
| 1065 | 9 | 0.013005592 |
| 1417 | 9 | 0.013005592 |
| 1568 | 9 | 0.013005592 |
| 1613 | 9 | 0.013005592 |
| 1644 | 9 | 0.013005592 |
| 1778 | 9 | 0.013005592 |
| 1806 | 9 | 0.013005592 |
| 1858 | 9 | 0.013005592 |
| 1892 | 9 | 0.013005592 |
| 1925 | 9 | 0.013005592 |
| 1950 | 9 | 0.013005592 |
| 2017 | 9 | 0.013005592 |
| 2048 | 9 | 0.013005592 |
| 2176 | 9 | 0.013005592 |
| 2463 | 9 | 0.013005592 |
| 2580 | 9 | 0.013005592 |
| 2616 | 9 | 0.013005592 |
| 2694 | 9 | 0.013005592 |
| 6726 | 9 | 0.013005592 |
| 10956 | 9 | 0.013005592 |
| 111 | 8 | 0.011560527 |
| 292 | 8 | 0.011560527 |
| 310 | 8 | 0.011560527 |
| 332 | 8 | 0.011560527 |
| 343 | 8 | 0.011560527 |
| 431 | 8 | 0.011560527 |
| 633 | 8 | 0.011560527 |
| 639 | 8 | 0.011560527 |
| 716 | 8 | 0.011560527 |
| 765 | 8 | 0.011560527 |
| 813 | 8 | 0.011560527 |
| 878 | 8 | 0.011560527 |
| 899 | 8 | 0.011560527 |
| 911 | 8 | 0.011560527 |
| 932 | 8 | 0.011560527 |
| 1016 | 8 | 0.011560527 |
| 1019 | 8 | 0.011560527 |
| 1081 | 8 | 0.011560527 |
| 1146 | 8 | 0.011560527 |
| 1192 | 8 | 0.011560527 |
| 1202 | 8 | 0.011560527 |
| 1248 | 8 | 0.011560527 |
| 1250 | 8 | 0.011560527 |
| 1279 | 8 | 0.011560527 |
| 1296 | 8 | 0.011560527 |
| 1411 | 8 | 0.011560527 |
| 1413 | 8 | 0.011560527 |
| 1704 | 8 | 0.011560527 |
| 1773 | 8 | 0.011560527 |
| 1840 | 8 | 0.011560527 |
| 1884 | 8 | 0.011560527 |
| 1923 | 8 | 0.011560527 |
| 1931 | 8 | 0.011560527 |
| 2015 | 8 | 0.011560527 |
| 2087 | 8 | 0.011560527 |
| 2128 | 8 | 0.011560527 |
| 2132 | 8 | 0.011560527 |
| 2202 | 8 | 0.011560527 |
| 2205 | 8 | 0.011560527 |
| 2262 | 8 | 0.011560527 |
| 2698 | 8 | 0.011560527 |
| 2772 | 8 | 0.011560527 |
| 2784 | 8 | 0.011560527 |
| 3246 | 8 | 0.011560527 |
| 5755 | 8 | 0.011560527 |
| 6359 | 8 | 0.011560527 |
| 7730 | 8 | 0.011560527 |
| 10009 | 8 | 0.011560527 |
| 11458 | 8 | 0.011560527 |
| 13197 | 8 | 0.011560527 |
| 14475 | 8 | 0.011560527 |
| 15549 | 8 | 0.011560527 |
| 16018 | 8 | 0.011560527 |
| 48 | 7 | 0.010115461 |
| 91 | 7 | 0.010115461 |
| 113 | 7 | 0.010115461 |
| 130 | 7 | 0.010115461 |
| 135 | 7 | 0.010115461 |
| 147 | 7 | 0.010115461 |
| 166 | 7 | 0.010115461 |
| 215 | 7 | 0.010115461 |
| 238 | 7 | 0.010115461 |
| 243 | 7 | 0.010115461 |
| 297 | 7 | 0.010115461 |
| 382 | 7 | 0.010115461 |
| 394 | 7 | 0.010115461 |
| 407 | 7 | 0.010115461 |
| 438 | 7 | 0.010115461 |
| 496 | 7 | 0.010115461 |
| 551 | 7 | 0.010115461 |
| 560 | 7 | 0.010115461 |
| 654 | 7 | 0.010115461 |
| 691 | 7 | 0.010115461 |
| 709 | 7 | 0.010115461 |
| 721 | 7 | 0.010115461 |
| 760 | 7 | 0.010115461 |
| 802 | 7 | 0.010115461 |
| 881 | 7 | 0.010115461 |
| 935 | 7 | 0.010115461 |
| 958 | 7 | 0.010115461 |
| 998 | 7 | 0.010115461 |
| 1003 | 7 | 0.010115461 |
| 1165 | 7 | 0.010115461 |
| 1286 | 7 | 0.010115461 |
| 1287 | 7 | 0.010115461 |
| 1292 | 7 | 0.010115461 |
| 1394 | 7 | 0.010115461 |
| 1409 | 7 | 0.010115461 |
| 1498 | 7 | 0.010115461 |
| 1511 | 7 | 0.010115461 |
| 1558 | 7 | 0.010115461 |
| 1586 | 7 | 0.010115461 |
| 1696 | 7 | 0.010115461 |
| 1713 | 7 | 0.010115461 |
| 1722 | 7 | 0.010115461 |
| 1737 | 7 | 0.010115461 |
| 1753 | 7 | 0.010115461 |
| 1776 | 7 | 0.010115461 |
| 1827 | 7 | 0.010115461 |
| 1860 | 7 | 0.010115461 |
| 1878 | 7 | 0.010115461 |
| 1879 | 7 | 0.010115461 |
| 1883 | 7 | 0.010115461 |
| 1949 | 7 | 0.010115461 |
| 1976 | 7 | 0.010115461 |
| 1978 | 7 | 0.010115461 |
| 1993 | 7 | 0.010115461 |
| 2074 | 7 | 0.010115461 |
| 2097 | 7 | 0.010115461 |
| 2133 | 7 | 0.010115461 |
| 2167 | 7 | 0.010115461 |
| 2204 | 7 | 0.010115461 |
| 2280 | 7 | 0.010115461 |
| 2293 | 7 | 0.010115461 |
| 2328 | 7 | 0.010115461 |
| 2349 | 7 | 0.010115461 |
| 2557 | 7 | 0.010115461 |
| 2562 | 7 | 0.010115461 |
| 2581 | 7 | 0.010115461 |
| 2588 | 7 | 0.010115461 |
| 2595 | 7 | 0.010115461 |
| 2596 | 7 | 0.010115461 |
| 2622 | 7 | 0.010115461 |
| 2633 | 7 | 0.010115461 |
| 2649 | 7 | 0.010115461 |
| 2662 | 7 | 0.010115461 |
| 2666 | 7 | 0.010115461 |
| 2687 | 7 | 0.010115461 |
| 2695 | 7 | 0.010115461 |
| 2705 | 7 | 0.010115461 |
| 2732 | 7 | 0.010115461 |
| 2757 | 7 | 0.010115461 |
| 7255 | 7 | 0.010115461 |
| 8006 | 7 | 0.010115461 |
| 8669 | 7 | 0.010115461 |
| 8803 | 7 | 0.010115461 |
| 9857 | 7 | 0.010115461 |
| 10844 | 7 | 0.010115461 |
| 11040 | 7 | 0.010115461 |
| 0 | 6 | 0.008670395 |
| 19 | 6 | 0.008670395 |
| 180 | 6 | 0.008670395 |
| 202 | 6 | 0.008670395 |
| 205 | 6 | 0.008670395 |
| 209 | 6 | 0.008670395 |
| 222 | 6 | 0.008670395 |
| 252 | 6 | 0.008670395 |
| 295 | 6 | 0.008670395 |
| 339 | 6 | 0.008670395 |
| 348 | 6 | 0.008670395 |
| 360 | 6 | 0.008670395 |
| 365 | 6 | 0.008670395 |
| 369 | 6 | 0.008670395 |
| 453 | 6 | 0.008670395 |
| 454 | 6 | 0.008670395 |
| 540 | 6 | 0.008670395 |
| 578 | 6 | 0.008670395 |
| 583 | 6 | 0.008670395 |
| 608 | 6 | 0.008670395 |
| 623 | 6 | 0.008670395 |
| 669 | 6 | 0.008670395 |
| 727 | 6 | 0.008670395 |
| 746 | 6 | 0.008670395 |
| 801 | 6 | 0.008670395 |
| 804 | 6 | 0.008670395 |
| 836 | 6 | 0.008670395 |
| 855 | 6 | 0.008670395 |
| 928 | 6 | 0.008670395 |
| 971 | 6 | 0.008670395 |
| 1015 | 6 | 0.008670395 |
| 1076 | 6 | 0.008670395 |
| 1112 | 6 | 0.008670395 |
| 1186 | 6 | 0.008670395 |
| 1234 | 6 | 0.008670395 |
| 1251 | 6 | 0.008670395 |
| 1260 | 6 | 0.008670395 |
| 1328 | 6 | 0.008670395 |
| 1342 | 6 | 0.008670395 |
| 1433 | 6 | 0.008670395 |
| 1448 | 6 | 0.008670395 |
| 1460 | 6 | 0.008670395 |
| 1473 | 6 | 0.008670395 |
| 1523 | 6 | 0.008670395 |
| 1600 | 6 | 0.008670395 |
| 1623 | 6 | 0.008670395 |
| 1648 | 6 | 0.008670395 |
| 1669 | 6 | 0.008670395 |
| 1736 | 6 | 0.008670395 |
| 1765 | 6 | 0.008670395 |
| 1766 | 6 | 0.008670395 |
| 1782 | 6 | 0.008670395 |
| 1785 | 6 | 0.008670395 |
| 1814 | 6 | 0.008670395 |
| 1817 | 6 | 0.008670395 |
| 1828 | 6 | 0.008670395 |
| 1861 | 6 | 0.008670395 |
| 1895 | 6 | 0.008670395 |
| 1985 | 6 | 0.008670395 |
| 2008 | 6 | 0.008670395 |
| 2013 | 6 | 0.008670395 |
| 2039 | 6 | 0.008670395 |
| 2041 | 6 | 0.008670395 |
| 2177 | 6 | 0.008670395 |
| 2184 | 6 | 0.008670395 |
| 2196 | 6 | 0.008670395 |
| 2200 | 6 | 0.008670395 |
| 2213 | 6 | 0.008670395 |
| 2276 | 6 | 0.008670395 |
| 2334 | 6 | 0.008670395 |
| 2336 | 6 | 0.008670395 |
| 2353 | 6 | 0.008670395 |
| 2359 | 6 | 0.008670395 |
| 2437 | 6 | 0.008670395 |
| 2472 | 6 | 0.008670395 |
| 2570 | 6 | 0.008670395 |
| 2578 | 6 | 0.008670395 |
| 2579 | 6 | 0.008670395 |
| 2606 | 6 | 0.008670395 |
| 2639 | 6 | 0.008670395 |
| 2676 | 6 | 0.008670395 |
| 2697 | 6 | 0.008670395 |
| 2734 | 6 | 0.008670395 |
| 2761 | 6 | 0.008670395 |
| 5468 | 6 | 0.008670395 |
| 5715 | 6 | 0.008670395 |
| 7196 | 6 | 0.008670395 |
| 7504 | 6 | 0.008670395 |
| 9550 | 6 | 0.008670395 |
| 9553 | 6 | 0.008670395 |
| 9590 | 6 | 0.008670395 |
| 9842 | 6 | 0.008670395 |
| 12042 | 6 | 0.008670395 |
| 13491 | 6 | 0.008670395 |
| 14419 | 6 | 0.008670395 |
| 14735 | 6 | 0.008670395 |
| 14997 | 6 | 0.008670395 |
| 15353 | 6 | 0.008670395 |
| 3 | 5 | 0.007225329 |
| 6 | 5 | 0.007225329 |
| 30 | 5 | 0.007225329 |
| 53 | 5 | 0.007225329 |
| 62 | 5 | 0.007225329 |
| 93 | 5 | 0.007225329 |
| 110 | 5 | 0.007225329 |
| 115 | 5 | 0.007225329 |
| 137 | 5 | 0.007225329 |
| 169 | 5 | 0.007225329 |
| 184 | 5 | 0.007225329 |
| 192 | 5 | 0.007225329 |
| 206 | 5 | 0.007225329 |
| 226 | 5 | 0.007225329 |
| 245 | 5 | 0.007225329 |
| 275 | 5 | 0.007225329 |
| 318 | 5 | 0.007225329 |
| 329 | 5 | 0.007225329 |
| 372 | 5 | 0.007225329 |
| 373 | 5 | 0.007225329 |
| 428 | 5 | 0.007225329 |
| 443 | 5 | 0.007225329 |
| 456 | 5 | 0.007225329 |
| 459 | 5 | 0.007225329 |
| 580 | 5 | 0.007225329 |
| 589 | 5 | 0.007225329 |
| 590 | 5 | 0.007225329 |
| 596 | 5 | 0.007225329 |
| 607 | 5 | 0.007225329 |
| 625 | 5 | 0.007225329 |
| 634 | 5 | 0.007225329 |
| 649 | 5 | 0.007225329 |
| 736 | 5 | 0.007225329 |
| 748 | 5 | 0.007225329 |
| 780 | 5 | 0.007225329 |
| 835 | 5 | 0.007225329 |
| 851 | 5 | 0.007225329 |
| 879 | 5 | 0.007225329 |
| 929 | 5 | 0.007225329 |
| 974 | 5 | 0.007225329 |
| 980 | 5 | 0.007225329 |
| 1022 | 5 | 0.007225329 |
| 1050 | 5 | 0.007225329 |
| 1069 | 5 | 0.007225329 |
| 1071 | 5 | 0.007225329 |
| 1079 | 5 | 0.007225329 |
| 1098 | 5 | 0.007225329 |
| 1113 | 5 | 0.007225329 |
| 1171 | 5 | 0.007225329 |
| 1197 | 5 | 0.007225329 |
| 1271 | 5 | 0.007225329 |
| 1280 | 5 | 0.007225329 |
| 1288 | 5 | 0.007225329 |
| 1319 | 5 | 0.007225329 |
| 1331 | 5 | 0.007225329 |
| 1355 | 5 | 0.007225329 |
| 1375 | 5 | 0.007225329 |
| 1410 | 5 | 0.007225329 |
| 1468 | 5 | 0.007225329 |
| 1527 | 5 | 0.007225329 |
| 1553 | 5 | 0.007225329 |
| 1556 | 5 | 0.007225329 |
| 1571 | 5 | 0.007225329 |
| 1572 | 5 | 0.007225329 |
| 1583 | 5 | 0.007225329 |
| 1589 | 5 | 0.007225329 |
| 1625 | 5 | 0.007225329 |
| 1626 | 5 | 0.007225329 |
| 1651 | 5 | 0.007225329 |
| 1676 | 5 | 0.007225329 |
| 1734 | 5 | 0.007225329 |
| 1755 | 5 | 0.007225329 |
| 1795 | 5 | 0.007225329 |
| 1812 | 5 | 0.007225329 |
| 1876 | 5 | 0.007225329 |
| 1918 | 5 | 0.007225329 |
| 1944 | 5 | 0.007225329 |
| 1953 | 5 | 0.007225329 |
| 1966 | 5 | 0.007225329 |
| 1975 | 5 | 0.007225329 |
| 1986 | 5 | 0.007225329 |
| 2007 | 5 | 0.007225329 |
| 2024 | 5 | 0.007225329 |
| 2025 | 5 | 0.007225329 |
| 2040 | 5 | 0.007225329 |
| 2090 | 5 | 0.007225329 |
| 2095 | 5 | 0.007225329 |
| 2156 | 5 | 0.007225329 |
| 2159 | 5 | 0.007225329 |
| 2178 | 5 | 0.007225329 |
| 2191 | 5 | 0.007225329 |
| 2194 | 5 | 0.007225329 |
| 2287 | 5 | 0.007225329 |
| 2309 | 5 | 0.007225329 |
| 2431 | 5 | 0.007225329 |
| 2449 | 5 | 0.007225329 |
| 2467 | 5 | 0.007225329 |
| 2468 | 5 | 0.007225329 |
| 2508 | 5 | 0.007225329 |
| 2511 | 5 | 0.007225329 |
| 2584 | 5 | 0.007225329 |
| 2592 | 5 | 0.007225329 |
| 2602 | 5 | 0.007225329 |
| 2617 | 5 | 0.007225329 |
| 2637 | 5 | 0.007225329 |
| 2658 | 5 | 0.007225329 |
| 2692 | 5 | 0.007225329 |
| 2750 | 5 | 0.007225329 |
| 2782 | 5 | 0.007225329 |
| 2799 | 5 | 0.007225329 |
| 3034 | 5 | 0.007225329 |
| 3094 | 5 | 0.007225329 |
| 4547 | 5 | 0.007225329 |
| 4744 | 5 | 0.007225329 |
| 4828 | 5 | 0.007225329 |
| 5319 | 5 | 0.007225329 |
| 6343 | 5 | 0.007225329 |
| 6877 | 5 | 0.007225329 |
| 7268 | 5 | 0.007225329 |
| 7620 | 5 | 0.007225329 |
| 8802 | 5 | 0.007225329 |
| 9805 | 5 | 0.007225329 |
| 10029 | 5 | 0.007225329 |
| 10611 | 5 | 0.007225329 |
| 11167 | 5 | 0.007225329 |
| 13108 | 5 | 0.007225329 |
| 14432 | 5 | 0.007225329 |
| 15958 | 5 | 0.007225329 |
| 16792 | 5 | 0.007225329 |
| 17194 | 5 | 0.007225329 |
| 22 | 4 | 0.005780263 |
| 38 | 4 | 0.005780263 |
| 56 | 4 | 0.005780263 |
| 77 | 4 | 0.005780263 |
| 112 | 4 | 0.005780263 |
| 191 | 4 | 0.005780263 |
| 203 | 4 | 0.005780263 |
| 213 | 4 | 0.005780263 |
| 267 | 4 | 0.005780263 |
| 321 | 4 | 0.005780263 |
| 322 | 4 | 0.005780263 |
| 338 | 4 | 0.005780263 |
| 345 | 4 | 0.005780263 |
| 384 | 4 | 0.005780263 |
| 403 | 4 | 0.005780263 |
| 416 | 4 | 0.005780263 |
| 422 | 4 | 0.005780263 |
| 430 | 4 | 0.005780263 |
| 477 | 4 | 0.005780263 |
| 486 | 4 | 0.005780263 |
| 490 | 4 | 0.005780263 |
| 497 | 4 | 0.005780263 |
| 512 | 4 | 0.005780263 |
| 524 | 4 | 0.005780263 |
| 557 | 4 | 0.005780263 |
| 559 | 4 | 0.005780263 |
| 571 | 4 | 0.005780263 |
| 611 | 4 | 0.005780263 |
| 655 | 4 | 0.005780263 |
| 665 | 4 | 0.005780263 |
| 677 | 4 | 0.005780263 |
| 693 | 4 | 0.005780263 |
| 729 | 4 | 0.005780263 |
| 764 | 4 | 0.005780263 |
| 769 | 4 | 0.005780263 |
| 770 | 4 | 0.005780263 |
| 790 | 4 | 0.005780263 |
| 800 | 4 | 0.005780263 |
| 848 | 4 | 0.005780263 |
| 978 | 4 | 0.005780263 |
| 984 | 4 | 0.005780263 |
| 1006 | 4 | 0.005780263 |
| 1043 | 4 | 0.005780263 |
| 1102 | 4 | 0.005780263 |
| 1134 | 4 | 0.005780263 |
| 1144 | 4 | 0.005780263 |
| 1145 | 4 | 0.005780263 |
| 1147 | 4 | 0.005780263 |
| 1162 | 4 | 0.005780263 |
| 1182 | 4 | 0.005780263 |
| 1184 | 4 | 0.005780263 |
| 1189 | 4 | 0.005780263 |
| 1195 | 4 | 0.005780263 |
| 1216 | 4 | 0.005780263 |
| 1226 | 4 | 0.005780263 |
| 1235 | 4 | 0.005780263 |
| 1321 | 4 | 0.005780263 |
| 1322 | 4 | 0.005780263 |
| 1343 | 4 | 0.005780263 |
| 1373 | 4 | 0.005780263 |
| 1396 | 4 | 0.005780263 |
| 1407 | 4 | 0.005780263 |
| 1422 | 4 | 0.005780263 |
| 1428 | 4 | 0.005780263 |
| 1440 | 4 | 0.005780263 |
| 1458 | 4 | 0.005780263 |
| 1475 | 4 | 0.005780263 |
| 1479 | 4 | 0.005780263 |
| 1487 | 4 | 0.005780263 |
| 1509 | 4 | 0.005780263 |
| 1529 | 4 | 0.005780263 |
| 1532 | 4 | 0.005780263 |
| 1537 | 4 | 0.005780263 |
| 1551 | 4 | 0.005780263 |
| 1554 | 4 | 0.005780263 |
| 1555 | 4 | 0.005780263 |
| 1575 | 4 | 0.005780263 |
| 1609 | 4 | 0.005780263 |
| 1620 | 4 | 0.005780263 |
| 1622 | 4 | 0.005780263 |
| 1624 | 4 | 0.005780263 |
| 1630 | 4 | 0.005780263 |
| 1647 | 4 | 0.005780263 |
| 1653 | 4 | 0.005780263 |
| 1660 | 4 | 0.005780263 |
| 1682 | 4 | 0.005780263 |
| 1694 | 4 | 0.005780263 |
| 1761 | 4 | 0.005780263 |
| 1781 | 4 | 0.005780263 |
| 1789 | 4 | 0.005780263 |
| 1792 | 4 | 0.005780263 |
| 1799 | 4 | 0.005780263 |
| 1804 | 4 | 0.005780263 |
| 1904 | 4 | 0.005780263 |
| 1909 | 4 | 0.005780263 |
| 1910 | 4 | 0.005780263 |
| 1947 | 4 | 0.005780263 |
| 1973 | 4 | 0.005780263 |
| 1989 | 4 | 0.005780263 |
| 2064 | 4 | 0.005780263 |
| 2093 | 4 | 0.005780263 |
| 2112 | 4 | 0.005780263 |
| 2126 | 4 | 0.005780263 |
| 2150 | 4 | 0.005780263 |
| 2197 | 4 | 0.005780263 |
| 2207 | 4 | 0.005780263 |
| 2209 | 4 | 0.005780263 |
| 2211 | 4 | 0.005780263 |
| 2239 | 4 | 0.005780263 |
| 2241 | 4 | 0.005780263 |
| 2268 | 4 | 0.005780263 |
| 2274 | 4 | 0.005780263 |
| 2311 | 4 | 0.005780263 |
| 2314 | 4 | 0.005780263 |
| 2318 | 4 | 0.005780263 |
| 2326 | 4 | 0.005780263 |
| 2333 | 4 | 0.005780263 |
| 2343 | 4 | 0.005780263 |
| 2379 | 4 | 0.005780263 |
| 2387 | 4 | 0.005780263 |
| 2405 | 4 | 0.005780263 |
| 2445 | 4 | 0.005780263 |
| 2446 | 4 | 0.005780263 |
| 2448 | 4 | 0.005780263 |
| 2462 | 4 | 0.005780263 |
| 2470 | 4 | 0.005780263 |
| 2504 | 4 | 0.005780263 |
| 2520 | 4 | 0.005780263 |
| 2521 | 4 | 0.005780263 |
| 2524 | 4 | 0.005780263 |
| 2526 | 4 | 0.005780263 |
| 2535 | 4 | 0.005780263 |
| 2573 | 4 | 0.005780263 |
| 2672 | 4 | 0.005780263 |
| 2682 | 4 | 0.005780263 |
| 2746 | 4 | 0.005780263 |
| 2754 | 4 | 0.005780263 |
| 2765 | 4 | 0.005780263 |
| 2766 | 4 | 0.005780263 |
| 2783 | 4 | 0.005780263 |
| 3047 | 4 | 0.005780263 |
| 3076 | 4 | 0.005780263 |
| 4641 | 4 | 0.005780263 |
| 4731 | 4 | 0.005780263 |
| 4733 | 4 | 0.005780263 |
| 4734 | 4 | 0.005780263 |
| 5373 | 4 | 0.005780263 |
| 5463 | 4 | 0.005780263 |
| 6175 | 4 | 0.005780263 |
| 6237 | 4 | 0.005780263 |
| 6241 | 4 | 0.005780263 |
| 6245 | 4 | 0.005780263 |
| 6307 | 4 | 0.005780263 |
| 6319 | 4 | 0.005780263 |
| 6411 | 4 | 0.005780263 |
| 6670 | 4 | 0.005780263 |
| 6727 | 4 | 0.005780263 |
| 6728 | 4 | 0.005780263 |
| 7052 | 4 | 0.005780263 |
| 7274 | 4 | 0.005780263 |
| 7630 | 4 | 0.005780263 |
| 7651 | 4 | 0.005780263 |
| 7714 | 4 | 0.005780263 |
| 8673 | 4 | 0.005780263 |
| 9439 | 4 | 0.005780263 |
| 10093 | 4 | 0.005780263 |
| 10168 | 4 | 0.005780263 |
| 10544 | 4 | 0.005780263 |
| 10668 | 4 | 0.005780263 |
| 12007 | 4 | 0.005780263 |
| 12497 | 4 | 0.005780263 |
| 12525 | 4 | 0.005780263 |
| 13897 | 4 | 0.005780263 |
| 14097 | 4 | 0.005780263 |
| 14424 | 4 | 0.005780263 |
| 14505 | 4 | 0.005780263 |
| 15613 | 4 | 0.005780263 |
| 15619 | 4 | 0.005780263 |
| 15999 | 4 | 0.005780263 |
| 16339 | 4 | 0.005780263 |
| 16495 | 4 | 0.005780263 |
| 16646 | 4 | 0.005780263 |
| 17201 | 4 | 0.005780263 |
| 26 | 3 | 0.004335197 |
| 55 | 3 | 0.004335197 |
| 64 | 3 | 0.004335197 |
| 66 | 3 | 0.004335197 |
| 76 | 3 | 0.004335197 |
| 90 | 3 | 0.004335197 |
| 100 | 3 | 0.004335197 |
| 104 | 3 | 0.004335197 |
| 106 | 3 | 0.004335197 |
| 109 | 3 | 0.004335197 |
| 139 | 3 | 0.004335197 |
| 153 | 3 | 0.004335197 |
| 173 | 3 | 0.004335197 |
| 174 | 3 | 0.004335197 |
| 182 | 3 | 0.004335197 |
| 187 | 3 | 0.004335197 |
| 194 | 3 | 0.004335197 |
| 204 | 3 | 0.004335197 |
| 212 | 3 | 0.004335197 |
| 214 | 3 | 0.004335197 |
| 218 | 3 | 0.004335197 |
| 227 | 3 | 0.004335197 |
| 248 | 3 | 0.004335197 |
| 249 | 3 | 0.004335197 |
| 273 | 3 | 0.004335197 |
| 281 | 3 | 0.004335197 |
| 285 | 3 | 0.004335197 |
| 312 | 3 | 0.004335197 |
| 313 | 3 | 0.004335197 |
| 326 | 3 | 0.004335197 |
| 357 | 3 | 0.004335197 |
| 366 | 3 | 0.004335197 |
| 377 | 3 | 0.004335197 |
| 386 | 3 | 0.004335197 |
| 393 | 3 | 0.004335197 |
| 395 | 3 | 0.004335197 |
| 400 | 3 | 0.004335197 |
| 425 | 3 | 0.004335197 |
| 440 | 3 | 0.004335197 |
| 445 | 3 | 0.004335197 |
| 448 | 3 | 0.004335197 |
| 458 | 3 | 0.004335197 |
| 464 | 3 | 0.004335197 |
| 465 | 3 | 0.004335197 |
| 474 | 3 | 0.004335197 |
| 507 | 3 | 0.004335197 |
| 519 | 3 | 0.004335197 |
| 530 | 3 | 0.004335197 |
| 537 | 3 | 0.004335197 |
| 552 | 3 | 0.004335197 |
| 555 | 3 | 0.004335197 |
| 556 | 3 | 0.004335197 |
| 563 | 3 | 0.004335197 |
| 565 | 3 | 0.004335197 |
| 582 | 3 | 0.004335197 |
| 591 | 3 | 0.004335197 |
| 597 | 3 | 0.004335197 |
| 603 | 3 | 0.004335197 |
| 604 | 3 | 0.004335197 |
| 609 | 3 | 0.004335197 |
| 614 | 3 | 0.004335197 |
| 627 | 3 | 0.004335197 |
| 630 | 3 | 0.004335197 |
| 643 | 3 | 0.004335197 |
| 651 | 3 | 0.004335197 |
| 689 | 3 | 0.004335197 |
| 701 | 3 | 0.004335197 |
| 745 | 3 | 0.004335197 |
| 753 | 3 | 0.004335197 |
| 755 | 3 | 0.004335197 |
| 779 | 3 | 0.004335197 |
| 792 | 3 | 0.004335197 |
| 798 | 3 | 0.004335197 |
| 809 | 3 | 0.004335197 |
| 821 | 3 | 0.004335197 |
| 826 | 3 | 0.004335197 |
| 843 | 3 | 0.004335197 |
| 862 | 3 | 0.004335197 |
| 867 | 3 | 0.004335197 |
| 871 | 3 | 0.004335197 |
| 882 | 3 | 0.004335197 |
| 883 | 3 | 0.004335197 |
| 902 | 3 | 0.004335197 |
| 905 | 3 | 0.004335197 |
| 939 | 3 | 0.004335197 |
| 942 | 3 | 0.004335197 |
| 947 | 3 | 0.004335197 |
| 970 | 3 | 0.004335197 |
| 992 | 3 | 0.004335197 |
| 1002 | 3 | 0.004335197 |
| 1031 | 3 | 0.004335197 |
| 1041 | 3 | 0.004335197 |
| 1042 | 3 | 0.004335197 |
| 1047 | 3 | 0.004335197 |
| 1064 | 3 | 0.004335197 |
| 1075 | 3 | 0.004335197 |
| 1087 | 3 | 0.004335197 |
| 1088 | 3 | 0.004335197 |
| 1089 | 3 | 0.004335197 |
| 1103 | 3 | 0.004335197 |
| 1108 | 3 | 0.004335197 |
| 1115 | 3 | 0.004335197 |
| 1117 | 3 | 0.004335197 |
| 1127 | 3 | 0.004335197 |
| 1128 | 3 | 0.004335197 |
| 1139 | 3 | 0.004335197 |
| 1151 | 3 | 0.004335197 |
| 1157 | 3 | 0.004335197 |
| 1213 | 3 | 0.004335197 |
| 1218 | 3 | 0.004335197 |
| 1219 | 3 | 0.004335197 |
| 1223 | 3 | 0.004335197 |
| 1240 | 3 | 0.004335197 |
| 1241 | 3 | 0.004335197 |
| 1256 | 3 | 0.004335197 |
| 1264 | 3 | 0.004335197 |
| 1281 | 3 | 0.004335197 |
| 1282 | 3 | 0.004335197 |
| 1294 | 3 | 0.004335197 |
| 1302 | 3 | 0.004335197 |
| 1304 | 3 | 0.004335197 |
| 1308 | 3 | 0.004335197 |
| 1311 | 3 | 0.004335197 |
| 1360 | 3 | 0.004335197 |
| 1369 | 3 | 0.004335197 |
| 1382 | 3 | 0.004335197 |
| 1383 | 3 | 0.004335197 |
| 1385 | 3 | 0.004335197 |
| 1437 | 3 | 0.004335197 |
| 1494 | 3 | 0.004335197 |
| 1520 | 3 | 0.004335197 |
| 1524 | 3 | 0.004335197 |
| 1526 | 3 | 0.004335197 |
| 1531 | 3 | 0.004335197 |
| 1541 | 3 | 0.004335197 |
| 1545 | 3 | 0.004335197 |
| 1546 | 3 | 0.004335197 |
| 1552 | 3 | 0.004335197 |
| 1566 | 3 | 0.004335197 |
| 1570 | 3 | 0.004335197 |
| 1576 | 3 | 0.004335197 |
| 1581 | 3 | 0.004335197 |
| 1598 | 3 | 0.004335197 |
| 1602 | 3 | 0.004335197 |
| 1633 | 3 | 0.004335197 |
| 1652 | 3 | 0.004335197 |
| 1657 | 3 | 0.004335197 |
| 1672 | 3 | 0.004335197 |
| 1675 | 3 | 0.004335197 |
| 1680 | 3 | 0.004335197 |
| 1706 | 3 | 0.004335197 |
| 1709 | 3 | 0.004335197 |
| 1746 | 3 | 0.004335197 |
| 1801 | 3 | 0.004335197 |
| 1819 | 3 | 0.004335197 |
| 1824 | 3 | 0.004335197 |
| 1826 | 3 | 0.004335197 |
| 1835 | 3 | 0.004335197 |
| 1854 | 3 | 0.004335197 |
| 1885 | 3 | 0.004335197 |
| 1896 | 3 | 0.004335197 |
| 1899 | 3 | 0.004335197 |
| 1902 | 3 | 0.004335197 |
| 1911 | 3 | 0.004335197 |
| 1932 | 3 | 0.004335197 |
| 1934 | 3 | 0.004335197 |
| 1942 | 3 | 0.004335197 |
| 1948 | 3 | 0.004335197 |
| 1968 | 3 | 0.004335197 |
| 1970 | 3 | 0.004335197 |
| 1971 | 3 | 0.004335197 |
| 1980 | 3 | 0.004335197 |
| 1982 | 3 | 0.004335197 |
| 1984 | 3 | 0.004335197 |
| 2021 | 3 | 0.004335197 |
| 2023 | 3 | 0.004335197 |
| 2033 | 3 | 0.004335197 |
| 2044 | 3 | 0.004335197 |
| 2046 | 3 | 0.004335197 |
| 2058 | 3 | 0.004335197 |
| 2061 | 3 | 0.004335197 |
| 2084 | 3 | 0.004335197 |
| 2138 | 3 | 0.004335197 |
| 2145 | 3 | 0.004335197 |
| 2158 | 3 | 0.004335197 |
| 2166 | 3 | 0.004335197 |
| 2189 | 3 | 0.004335197 |
| 2195 | 3 | 0.004335197 |
| 2214 | 3 | 0.004335197 |
| 2217 | 3 | 0.004335197 |
| 2223 | 3 | 0.004335197 |
| 2225 | 3 | 0.004335197 |
| 2288 | 3 | 0.004335197 |
| 2296 | 3 | 0.004335197 |
| 2298 | 3 | 0.004335197 |
| 2299 | 3 | 0.004335197 |
| 2300 | 3 | 0.004335197 |
| 2306 | 3 | 0.004335197 |
| 2322 | 3 | 0.004335197 |
| 2348 | 3 | 0.004335197 |
| 2350 | 3 | 0.004335197 |
| 2354 | 3 | 0.004335197 |
| 2356 | 3 | 0.004335197 |
| 2366 | 3 | 0.004335197 |
| 2393 | 3 | 0.004335197 |
| 2411 | 3 | 0.004335197 |
| 2428 | 3 | 0.004335197 |
| 2442 | 3 | 0.004335197 |
| 2471 | 3 | 0.004335197 |
| 2484 | 3 | 0.004335197 |
| 2485 | 3 | 0.004335197 |
| 2490 | 3 | 0.004335197 |
| 2493 | 3 | 0.004335197 |
| 2519 | 3 | 0.004335197 |
| 2567 | 3 | 0.004335197 |
| 2574 | 3 | 0.004335197 |
| 2620 | 3 | 0.004335197 |
| 2640 | 3 | 0.004335197 |
| 2663 | 3 | 0.004335197 |
| 2674 | 3 | 0.004335197 |
| 2683 | 3 | 0.004335197 |
| 2693 | 3 | 0.004335197 |
| 2696 | 3 | 0.004335197 |
| 2756 | 3 | 0.004335197 |
| 2767 | 3 | 0.004335197 |
| 2786 | 3 | 0.004335197 |
| 3028 | 3 | 0.004335197 |
| 3652 | 3 | 0.004335197 |
| 4147 | 3 | 0.004335197 |
| 4381 | 3 | 0.004335197 |
| 4773 | 3 | 0.004335197 |
| 4823 | 3 | 0.004335197 |
| 5248 | 3 | 0.004335197 |
| 6110 | 3 | 0.004335197 |
| 6341 | 3 | 0.004335197 |
| 6376 | 3 | 0.004335197 |
| 6591 | 3 | 0.004335197 |
| 6602 | 3 | 0.004335197 |
| 6668 | 3 | 0.004335197 |
| 7120 | 3 | 0.004335197 |
| 7348 | 3 | 0.004335197 |
| 7349 | 3 | 0.004335197 |
| 7634 | 3 | 0.004335197 |
| 7640 | 3 | 0.004335197 |
| 7741 | 3 | 0.004335197 |
| 8140 | 3 | 0.004335197 |
| 8175 | 3 | 0.004335197 |
| 8314 | 3 | 0.004335197 |
| 8376 | 3 | 0.004335197 |
| 8787 | 3 | 0.004335197 |
| 8805 | 3 | 0.004335197 |
| 9134 | 3 | 0.004335197 |
| 9260 | 3 | 0.004335197 |
| 9377 | 3 | 0.004335197 |
| 9555 | 3 | 0.004335197 |
| 9560 | 3 | 0.004335197 |
| 9636 | 3 | 0.004335197 |
| 9638 | 3 | 0.004335197 |
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| 17410 | 3 | 0.004335197 |
| 1 | 2 | 0.002890132 |
| 2 | 2 | 0.002890132 |
| 7 | 2 | 0.002890132 |
| 12 | 2 | 0.002890132 |
| 15 | 2 | 0.002890132 |
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| 21 | 2 | 0.002890132 |
| 40 | 2 | 0.002890132 |
| 51 | 2 | 0.002890132 |
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| 4 | 1 | 0.001445066 |
| 5 | 1 | 0.001445066 |
| 8 | 1 | 0.001445066 |
| 9 | 1 | 0.001445066 |
| 10 | 1 | 0.001445066 |
| 11 | 1 | 0.001445066 |
| 13 | 1 | 0.001445066 |
| 14 | 1 | 0.001445066 |
| 18 | 1 | 0.001445066 |
| 23 | 1 | 0.001445066 |
| 25 | 1 | 0.001445066 |
| 27 | 1 | 0.001445066 |
| 28 | 1 | 0.001445066 |
| 31 | 1 | 0.001445066 |
| 32 | 1 | 0.001445066 |
| 33 | 1 | 0.001445066 |
| 34 | 1 | 0.001445066 |
| 36 | 1 | 0.001445066 |
| 37 | 1 | 0.001445066 |
| 42 | 1 | 0.001445066 |
| 43 | 1 | 0.001445066 |
| 44 | 1 | 0.001445066 |
| 45 | 1 | 0.001445066 |
| 46 | 1 | 0.001445066 |
| 47 | 1 | 0.001445066 |
| 49 | 1 | 0.001445066 |
| 52 | 1 | 0.001445066 |
| 54 | 1 | 0.001445066 |
| 58 | 1 | 0.001445066 |
| 63 | 1 | 0.001445066 |
| 67 | 1 | 0.001445066 |
| 70 | 1 | 0.001445066 |
| 71 | 1 | 0.001445066 |
| 72 | 1 | 0.001445066 |
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| 80 | 1 | 0.001445066 |
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| 88 | 1 | 0.001445066 |
| 94 | 1 | 0.001445066 |
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| 102 | 1 | 0.001445066 |
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| 107 | 1 | 0.001445066 |
| 120 | 1 | 0.001445066 |
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| 239 | 1 | 0.001445066 |
| 240 | 1 | 0.001445066 |
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| 1637 | 1 | 0.001445066 |
| 1639 | 1 | 0.001445066 |
| 1640 | 1 | 0.001445066 |
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| 1707 | 1 | 0.001445066 |
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| 1856 | 1 | 0.001445066 |
| 1857 | 1 | 0.001445066 |
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| 1881 | 1 | 0.001445066 |
| 1886 | 1 | 0.001445066 |
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| 1889 | 1 | 0.001445066 |
| 1890 | 1 | 0.001445066 |
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| 1893 | 1 | 0.001445066 |
| 1894 | 1 | 0.001445066 |
| 1898 | 1 | 0.001445066 |
| 1906 | 1 | 0.001445066 |
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| 1908 | 1 | 0.001445066 |
| 1913 | 1 | 0.001445066 |
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| 1927 | 1 | 0.001445066 |
| 1929 | 1 | 0.001445066 |
| 1930 | 1 | 0.001445066 |
| 1933 | 1 | 0.001445066 |
| 1936 | 1 | 0.001445066 |
| 1939 | 1 | 0.001445066 |
| 1940 | 1 | 0.001445066 |
| 1943 | 1 | 0.001445066 |
| 1945 | 1 | 0.001445066 |
| 1946 | 1 | 0.001445066 |
| 1951 | 1 | 0.001445066 |
| 1952 | 1 | 0.001445066 |
| 1954 | 1 | 0.001445066 |
| 1955 | 1 | 0.001445066 |
| 1957 | 1 | 0.001445066 |
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| 1969 | 1 | 0.001445066 |
| 1974 | 1 | 0.001445066 |
| 1981 | 1 | 0.001445066 |
| 1983 | 1 | 0.001445066 |
| 1987 | 1 | 0.001445066 |
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| 1991 | 1 | 0.001445066 |
| 1992 | 1 | 0.001445066 |
| 1996 | 1 | 0.001445066 |
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the_tate %>% dplyr::filter(artistId %in% c(558,2121)) %>% dplyr::select(artistId,artist) %>% distinct(artistId,artist) # A tibble: 2 × 2
artistId artist
<dbl> <chr>
1 558 Turner, Joseph Mallord William
2 2121 Warhol, Andy The artist with the most works in the Tate collection is Turner, Joseph Mallord William with artistId 558.
The artist with the tenth-most works in the Tate collection is Warhol, Andy with artistId = 2121.
Exercise 4
The artist with the greatest number of works in the Tate collection represent 56.919697692% of the total number of works
Exercise 5
total_artist_title_pairs <- the_tate %>% dplyr::select(artistId , title) %>% tibble::as_tibble() %>% count()
total_artist_title_pairs_distinct <- the_tate %>% dplyr::select(artistId , title) %>% dplyr::distinct() %>% count()
#No. of Total Rows
print(total_artist_title_pairs)# A tibble: 1 × 1
n
<int>
1 69201#No. of Distinct Rows
print(total_artist_title_pairs_distinct)# A tibble: 1 × 1
n
<int>
1 45496#No. of Duplicate Rows
print(total_artist_title_pairs - total_artist_title_pairs_distinct) n
1 23705There are 23705 duplicate artist-title pairs
Exercise 6
the_tate_area <- the_tate %>% dplyr::select(artist,artistId,width,height) %>% dplyr::mutate(area = (width*height)/100) %>% tidyr::drop_na(area) %>% dplyr::arrange(desc(area))
dplyr::slice_head(the_tate_area)# A tibble: 1 × 5
artist artistId width height area
<chr> <dbl> <dbl> <dbl> <dbl>
1 Therrien, Robert 2312 8920 14850 1324620dplyr::slice_tail(the_tate_area)# A tibble: 1 × 5
artist artistId width height area
<chr> <dbl> <dbl> <dbl> <dbl>
1 Mesens, E.L.T. 1624 3 79 2.37The artist with the largest work in the tate collection is Therrien, Robert
The artist with the smallest work in the collection is Mesens, E.L.T.. The smallest work has area 2.37 \(\text{cm}^2\)
Exercise 7
joined_data <- the_tate %>% dplyr::left_join(the_tate_artists, by = join_by(artistId == id)) %>% tidyr::drop_na(gender)
joined_data <- joined_data %>% dplyr::group_by(gender)
view(joined_data)Exercise 8
spx_historical_data <- readr::read_delim("data/SPX_HistoricalData_1692322132002.csv", ",", escape_double = FALSE, trim_ws = TRUE)Rows: 1257 Columns: 6
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Date, Volume
dbl (4): Close/Last, Open, High, Low
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.view(spx_historical_data)#Create mutated tibble where daily return and variance are calculated fields and remove null
spx_historical_mutated <- spx_historical_data %>% dplyr::mutate(year = lubridate::year(mdy(Date))) %>% dplyr::arrange(desc(lubridate::date(mdy(Date)))) %>% dplyr::mutate(daily_return =log10(`Close/Last`/dplyr::lead(`Close/Last`))) %>% dplyr::mutate(variance = daily_return*daily_return) %>% tidyr::drop_na(daily_return)
#Take log sum as annual return and sqrt of sum of variance as annual deviation
spx_historical_summary <- spx_historical_mutated %>% dplyr::group_by(year) %>% dplyr::summarize(
annual_return = sum(daily_return)*100,
std_dev = sqrt(sum(variance))*100,
.groups = "drop"
)
spx_historical_summary# A tibble: 6 × 3
year annual_return std_dev
<dbl> <dbl> <dbl>
1 2018 -5.57 5.25
2 2019 11.0 5.46
3 2020 6.54 15.1
4 2021 10.3 5.72
5 2022 -9.39 10.5
6 2023 5.96 4.66view(spx_historical_mutated)The annual return in the SPX price in 2020 was 6.542629%.
The corresponding price volatility was 15.070205%.
Exercise 9
period_return <- sum(spx_historical_summary$annual_return)
period_volatility <- sqrt(sum(spx_historical_summary$std_dev^2))
new_row <- tibble::tibble(year = "Period",annual_return = period_return,std_dev = period_volatility)
spx_historical_summary <- spx_historical_summary %>% dplyr::mutate(year = as.character(year))
spx_historical_summary = bind_rows(spx_historical_summary,new_row)
spx_historical_summary <- gt(spx_historical_summary)
spx_historical_summary <-
spx_historical_summary %>%
tab_header(
title = "SPX Summary Table",
)
spx_historical_summary| SPX Summary Table | ||
| year | annual_return | std_dev |
|---|---|---|
| 2018 | -5.573632 | 5.253895 |
| 2019 | 11.017904 | 5.456396 |
| 2020 | 6.542629 | 15.070205 |
| 2021 | 10.343676 | 5.717498 |
| 2022 | -9.389577 | 10.481097 |
| 2023 | 5.960518 | 4.664770 |
| Period | 18.901518 | 21.184664 |
The period volatility was 21.184664%